The fast Hartley transform (FHT) is a new tool for converting data between time and frequency domains. In this thesis, some speed-optimized software implementations of the radix-2 and split-radix FHT algorithms are presented initially, and then applied to the problems of convolution, computation of power spectra, image degradation, and image restoration. Subsequent work involved the development of a new bit-reversal algorithm. This algorithm is fast and efficient, and can be used to increase the throughput of the FHT. Finally, several hardware implementations are presented for the discrete Hartley transform (DHT) and the FHT with architectures using a single butterfly unit, pipelining and superparallelism. The advantages of each implementation are stressed. The data processing rates of these hardware implementations are analyzed. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate